# 401-4915-00L Risk Theory for Insurance

Semester | Autumn Semester 2013 |

Lecturers | M. V. Wüthrich |

Periodicity | yearly course |

Language of instruction | English |

Abstract | This course gives an introduction to insurance risk theory. It serves as a basis for later courses on non-life insurance mathematics, risk management (in finance) and re-insurance. Topics included are claims processes, models for claims frequency and severity, ruin theory, modelling of large claims. |

Objective | The student is familiar with the basics of non-life insurance premium calculation. Moreover, he knows the basic results in ruin theory and is able to distinguish short-tailed claims behaviour from heavy-tailed claims behaviour. |

Content | The following topics are treated: 1. The Basic Insurance Claims Model 2. Premium Calculation Principles 2. Models for the Claims Number Process 3. Models for Claims Severity 4. The Total Claim Amount (TCA) Modelling 5. Approximations for the TCA Distributions 6. Ruin Theory 7. The Modelling of Large Claims |

Literature | Literature for further reading: - M. V. Wüthrich, Non-Life Insurance: Mathematics & Statistics http://ssrn.com/abstract=2319328 - H. Schmidli, Lecture Notes on Risk Theory http://www.math.ku.dk/~schmidli/rt.pdf - T. Mikosch (2004). Non-Life Insurance Mathematics. An Introduction with Stochastic Processes. Springer, Berlin. - S. Asmussen (2000). Ruin Probabilities. World Scientific, Singapore. - T. Rolski, H. Schmidli, V. Schmidt, J. Teugels (1999). Stochastic Processes for Insurance and Finance. Wiley, Chichester. |

Prerequisites / Notice | The exams ONLY take place during the official ETH examination period. This course will be held in English and counts towards the diploma of "Aktuar SAV". For the latter, see details under www.actuaries.ch. Prerequisites: knowledge of probability theory, statistics and applied stochastic processes. |